TN295 




No. 9261; 












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IC 9261 



BUREAU OF MINES 
INFORMATION CIRCULAR/1990 



Fire Location Model 



By John C. Edwards 




„ YEARS ,<>, 
^^AU OF ^' 



U.S. BUREAU OF MINES 
1910-1990 



THE MINERALS SOURCE 



Mission: Asthe Nation's principal conservation 
agency, the Department of the Interior has respon- 
sibility for most of our nationally-owned public 
lands and natural and cultural resources. This 
includes fostering wise useof our land and water 
resources, protecting our fish and wildlife, pre- 
serving the environmental and cultural values of 
our national parks and historical places, and pro- 
viding for the enjoyment of life through outdoor 
recreation. The Department assesses our energy 
and mineral resources and works to assure that 
their development is in the best interests of all 
our people. The Department also promotes the 
goals of the Take Pride in America campaign by 
encouraging stewardship and citizen responsibil- 
ity for the public lands and promoting citizen par- 
ticipation in their care. The Department also has 
a major responsibility for American Indian reser- 
vation communities and for people who live in 
Island Territories under U.S. Administration. 



Information Circular 9261 



Fire Location IVIodei 



By John C. Edwards 



UNITED STATES DEPARTMENT OF THE INTERIOR 
Manuel Lujan, Jr., Secretary 

BUREAU OF MINES 
T S Ary, Director 






^0' 






Library of Congress Cataloging in Publication Data: 



Edwards, John C. 

Fire location model / by John C. Edwards. 

p. cm. - (Information circular / Bureau of Mines; 9261) 

Includes bibliographical references (p. ). 

Supt. of Docs, no.: I 28.27:9261. 

1. Mine fires-Prevention and control-Data processing. 2. Smoke-Diffusion 
rate-Data processing. 3. FORTRAN (Computer program language) I. Title. II. 
Series. III. Series: Information circular (United States. Bureau of Mines); 9261. 

TN295.U4 [TN315] 622 s-dc20 [622'.82] 90-2096 

CIP 



CONTENTS 

Page 

Abstract 1 

Introduction 2 

Model description 2 

Application 3 

Conclusions 9 

Appendix-FORTRAN computer program 10 

ILLUSTRATIONS 

1. Mine ventilation plan 4 

2. Mesh structure for computer model 5 

3. Travel times for each jiirway 5 

4. Time lag for smoke detectors 7 

5. Partition of network into zones by lag time 8 

TABLES 

1. Input data file 3 

2. Airway dimensions 3 

3. Computer-generated minimum travel time paths 6 





UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT 


cfm 


cubic foot per minute 


min 


minute 


ft 


foot 


pet 


percent 


e 


square foot 







FIRE LOCATION MODEL 

By John C. Edwards^ 



ABSTRACT 

A fire location computational model was developed by the U.S. Bureau of Mines. The model can 
determine all the possible paths in a mine that smoke can travel from a fixed fire source to a smoke 
detector. The associated FORTRAN computer program can be utilized to determine the minimum 
travel time from a source fire to a smoke detector. The difference in travel time from an isolated fire 
source to two or more detectors can be used to isolate those airways in which the source fire is located. 



^Research physicist, Pittsburgh Research Center, U.S. Bureau of Mines, Pittsburgh, PA. 



INTRODUCTION 



The early detection of a fire in a mine is necessary for 
the informed implementation of miner evacuation. The 
placement of smoke detectors throughout the mine net- 
work is the obvious strategy to follow. In general, several 
detectors will be installed. The inherent complexity of 
the mine network, in the case of a metal or nonmetal 
mine, can pose a formidable problem for the interpretation 
of the signals received by several smoke detectors located 
throughout the mine network. The smoke from a source 
fire will travel with the mine ventilation, and be diluted at 
airway jimctions. The prediction of Jiirway ventilation in a 
mine network with the edrflow controlled by fans and natu- 
ral ventilation is amenable to computer generated solutions 
both for the 2drflow quantity and the concentration of the 
products of combustion that emanate from a fire source.^ 
If the mine ventilation is known, either measured or pre- 
dicted with the mine ventilation computer program,^ dif- 
ferences in arrivid times of smoke from a source fire to 
several detectors can be used to isolate the location of the 
fire. As part of its research program to develop a mine 
fire detection strategy, the U.S. Bureau of Mines devel- 
oped a FORTRAN computer program that can be used to 
determine the minimum travel time from a fire source to 
a smoke detector. This requires an enumeration by the 
program of all the possible paths available to the smoke. 
This approach, while a significant factor in the isolation of 



a mine fire location, is not without limitations. The total 
number of possible paths increases rapidly with an increase 
in the number of airways. The computations presented in 
this report are limited to paths that individuaUy consist of 
at most nine airways. However, the structure of the pro- 
gram permits an extension of the model to paths that are 
defined by any finite number of eiirways provided adequate 
computer memory is available. 

The model developed in this report has apphcations 
both in the planning for the location of detectors in a 
mine, and in the mine emergency stage. To determine 
the optimum location of fire detectors, the mine network 
can be divided into zones, each of which is associated with 
a difference in calculated smoke arrival time between a 
pair of detectors. For established mine ventilation, this 
promotes the efficient selection of detector sites. In the 
event of a fire, the information is then available to deter- 
mine in which zone the fire is located. This can assist in 
miner escape route planning. A fire can alter the ventila- 
tion, and possibly induce flow reversal. If the new ventila- 
tion produced by the fire can be quzmtified, then the pro- 
gram can be applied for the given distribution of detectors 
and new ventilation to isolate the zone in which the fire 
occurs. In practice, observations made within the mine in 
the event of a mine emergency can be used to further iso- 
late the zone in which the fire is located. 



MODEL DESCRIPTION 



The strategy of the model is to determine the differ- 
ence between signal (smoke) arrival times at several 
detectors. This should isolate the region of the mine in 
which the source fire is located. The mine network is rep- 
resented by a grid of airways that intersect at junctions. 
For the current model, it is assumed that each junction 
forms the intersection of exactly two airways. The network 
of intersecting airways is arranged as an intersection of M 
rows zmd N columns. This is possible since it is assimied 
that exactly four airways join at a junction. If less thzm 
four airways join at a jimction for a particular mine repre- 
sentation, then additional airways with zero airflow are 



Edwards, J. C, and R, E. Greuer. Real-Time Calculation of 
Product-of-Combustion Spread in a Multilevel Mine. BuMines IC 8901, 
1982, 117 pp. 

Edwards, J. C, and J. S. Li. Computer Simulation of Ventilation in 
Multilevel Mines. Paper in Proceedings, Third International Mine 
Ventilation Congress, Harrogate, England. Inst, of Min. and Metall., 
London, 1984, pp. 47-51. 

Orederkirk, S. J., W. H. Pomroy, J. C. Edwards, and J. Marks. 
Mine Stench Fire Warning Computer Model Development and In-Mine 
Validation Testing. Paper in Proceedings, Second U.S. Mine 
Ventilation Symposium (Univ. NV-Reno, Sept. 23-25, 1985), ed. by 
P. Mousset-Jones. Balkema, 1985, pp. 29-35. 

^First work cited in footnote 2. 



added to complete the matrix representation of the 
network. 

The approach is a systematic determination of all possi- 
ble paths from an assumed fire source location to the air- 
way designated as the detection airway. For a path con- 
taining a specified number of airways (I), there is a 
maximum of 4' distinct possible paths that emanate from 
a selected jimction. This might be visualized as a tree 
structure in which the termination of each limb is the 
source of four airways. Of these paths, a smaller nxmiber 
will contain the detection airway. Of the latter quantity, a 
further subset will be consistent with the established air- 
flow throughout the mine network. A specific application 
is for a fixed ventilation in the mine. If a flow reversal 
should occur as a resxilt of a fire, the program is applied 
for the new ventilation plan. From this last selected group, 
there will be a single path representative of the minimum 
travel time. The difference between the minimum travel 
times to two detectors from a fixed fire source at a speci- 
fied jimction is characteristic of a region of the network 
that may contain other such jimctions. To establish these 
regions, this procedure is repeated for each and every 
junction in the network. The evaluation of the minimum 
time travel paths is accomplished with the FORTRAN 
computer program in the appendix. 







Table 1. -Input data file 


■ BRANCH.DAT 


Card 


1 Column 


Format 


Symbol 


Definition 


1 


6-10 


15 


MSP 


Total number source junctions. 




16-20 


'5 


MST 


Total number detection airways. 


2 


1-80 


4(5x,l5)^ 


ISP 


Source junction numbers. 


3 


1-80 


4(5x,l5)^ 


1ST 


Detection ainway numbers. 


4 


6-10 


15 


NJ 


Number of junctions. 




16-20 


15 


NBT 


Number of airways. 




26-30 


15 


N 


Number of columns for 2d template. 




36-40 


15 


M 


Number of rows for 2d template. 


5^ . . . 


6-10 


15 


NO 


Airway number. 




16-20 


15 


NA 


Start junction for ainvay NC. 




26-30 


15 


NB 


Rnish junction for airway NC. 




33-43 


F10.5 


Q 


Volumetric airflow in ainway NC (cfm). 




46-56 


F10.5 


DS 


Length of airway NC (ft). 




59-64 


F5.1 


AR 


Cross-sectional area of airway NC (ft^). 



'Total required equals number of airways (NBT). 

^Defines four values, each with format 15 and separated by five blank spaces. 



It is already apparent that the Umiting characteristic of 
this model is the number of paths, 4', each of which 
contains I airways, that must be constructed by the com- 
puter program. This total coimt includes retracement 
along airways. The memory restrictions of the computer 
system for the application in this report have limited the 
definition of a path to at most nine airways. Each node in 
the network is the soiuce of 4' = 262,144 distinct paths. 
This restriction involves superfluous counting, and must 
be unproved upon in a subsequent effort. However, the 
method is accurate, and serves to demonstrate a strategy 
for smoke detection in a mine network. 

Utilization of the model requires the preparation of 
several templates (diagremis). The first template is a 
representation of the physical mine network by branches 
that intersect at nodes. The steady-state airflow for the 
mine network is either measured, or calculated with the 
mine ventilation computer program.* 



The second template is a relabelling of the mesh air- 
ways and junctions to make it compatible with the model 
format requirements for the computer program. As stated 
earUer, the jimctions aie. arremged in M rows and N 
columns. The junctions, MN in number, are ordered se- 
quentiadly with junctions 1, 2,..., N in the first row, 
junctions N+ l,N-i-2,...,2N in the second row, and junctions 
MN-N-i-l,MN-N-i-2,...,MN in the top row, row M. The 
junction numbers in the first column are 1,N+1,...,MN- 
N+1, in the second column aie junctions 2,N-I-2,...,MN- 
N+2, and the last coliunn, column N, is formed by jimc- 
tions N,2N,...,MN. Although the structiu-e of the mesh is 
critical from a program apphcation viewpoint, it is not 
necessary to maintain a proportionahty among airway 
lengths that scales with the junction separation distances. 
Table 1 shows the required format for the input data file, 
BRANCH.DAT. In the next section, an application is pre- 
sented that demonstrates the program utUity. 



APPLICATION 



Consider the mine ventilation plan for a section of a 
triple entry with crosscuts as shown in figure 1. The ven- 
tilation is established by a fan in airway No. 21. The 
dimensions of the jiirways are shown in table 2. For this 
study, because of the limitation upon the munber of air- 
ways that can constitute a path, only a section of the triple 
entry is considered. The ventilation plan was estabUshed 
with an application of the Bureau's ventilation computer 

program.' It was possible to eliminate junction 14 and 
combine airways 20 and 21 into a single cdrway in the ven- 
tilation plan prior to construction of the second template 
without any loss of information. 



First work cited in footnote 2. 
^First work cited in footnote 2. 



Table 2.-Alrway dimensions 



Airway 



1 . 

2 . 

3 . 

4 . 

5 . 

6 . 

7 . 

8 . 

9 . 
10 
11 
12 



DS, ft AR, ft^ 



5,000 

2,000 

2,000 

2,000 

200 

200 

2,000 

2,000 

200 

200 

2,000 

2,000 



54 
54 
54 
54 
36 
36 
54 
54 
36 
36 
54 
54 



Airway 



13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 



AR Cross-sectional area of airway. 
DS Length of airway. 



DS, ft AR, ft^ 



200 

200 

2,000 

2,000 

200 

200 

5,000 

4,990 

10 

200 

200 



36 
36 
54 
54 
36 
36 
54 
54 
54 
36 
36 



Qy 



(4) 



3,812 



3,812 



■^ 



(5) 



867 



2,355 



6h- 

1 1 



(6) 



(7) 



(9) 



1,456 



4> 



KEY 

V^ Junction 
(7) Airway 
^Airflow direction 



13,783 Airflow, cfm 



(3) 



2,944 



€> 



(2) 



6,420 



(II) 



9,365 



ay 



;i) 



(13) 



11,937 



3,259 



(b- 



(8) 



2,670 



t. 



(15) 



21,302 







(17) 



21,302 



(10) 



8,168 



2,355 



4) 



(12) 



4,418 



<t- 



(19) 



(22) 



(14) 



29,706 



22,186 



(18) 



21,302 



(21) 



(23) 



5,615 



A (16) A (20) ^^ (7 A 



; 43,488 



43.488 



Figure 1 .-Mine ventilation plan. 



The 22 branches and 15 junctions are renumbered to 
conform to the prescription for the second template 
(fig. 2). There are M = 3 rows and N=5 columns. The 
time of travel along each airway is calculated from the 
airway volumetric flow rate (O), airway length (DS), and 
airway cross-sectional area (AR). The airway travel times 
£U"e shown in figure 3. 

For the demonstration of the program's capability, 
airways 13, 22, and 14, were designated to contain de- 
tectors. The progrcun's evaluation of the minimum travel 
time paths, consisting of less thjm nine airways, which 
originate from each of the 15 junctions are enumerated in 
table 3. It was not possible to reach airway 14 from junc- 
tion 13 with a path composed of nine or less airways. 

These results must be treated with caution. Although 
the computer program as used in this apphcation will 
sccuch out minimum travel time paths composed of at 
most nine curways, there might be a path containing more 
than nine 2iirways that represents a smcdler travel time. 
Such is the case for the evaluation of the smoke travel 
time from junctions 1 and 6 to airway 13. Table 3 shows 
the minimum travel time path of 118.65 min from junction 
1 to ciirway 13 containing 7 airways, namely airways 5, 14, 



19, 15, 11, 12, and 13. However, the ll-airway path con- 
tainmg anways 5, 14, 19, 20, 21, 22, 18, 9, 4, 8, and 13, 
which represents a travel time of 113.29 min, is excluded. 
A similar problem occurs with junction 6. For junction 6, 
table 3 Usts the minimum travel time path containing 6 
airways: airways 14, 19, 15, 11, 12, and 13, and a travel 
time of 115.59 min. In actuality, the minimum travel time 
path consists of the 10 airways, airways 14, 19, 20, 21, 22, 
18, 9, 4, 8, and 13, and is associated with a travel time of 
110.23 min. In each of these exceptions, the relative error 
in the travel times is less than 5 pet. 

This exaunple poses the question as to the maximimi 
extent of the mesh formed from mine airways that can be 
considered without exceeding the constraint that the min- 
imum travel time path will not contain more than nine 
airways. This would remain a problem even if the con- 
straint of nine airways is increased. There is not a direct 
answer to this quandary. In this particular application, the 
total number of airways is 22, slightly greater than twice 
the maximum nine Jiirways that can be used to construct 
a path. The error involved affects less than 10 pet of the 
junctions, with an error in travel time of less than 5 pet for 
the affected junctions. This leads to the qualitative result 



(14) 






(5) 



(Z> 



19) 



;io) 



(1) 



KEY 

Q£) Junction 
(7) Airway 
^Airflow direction 



at 



(20) 



(15) 



<Z> 



(II) 



(6) 



2y^ 



(2) 



@- 



(21) 



(16) 






(12) 



(7) 



^ 



(3) 



^ 



(221 



(17) 



Qy 



(13) 



(8) 



<f> 



(4) 



Figure 2.-Mesh structure for computer model. 



■® 



(18) 



■m 



(9) 



4) 



45.86 



KEY 

6.21 Airway travel time, min 



28.33 


36.68 


11.53 


12.67 


1.89 


8.30 


1.12 


0.60 


74.18 


40.45 


24.44 


12.17 


3.06 


2.21 


0.88 


0.24 



19.23 7.84 6.21 

Figure 3.-Travel times for each airway. 



0.34 



0.17 



Table S.-Computer-generated minimum travel time paths 

Source junction Airway path (see fig. 2) Minimum travel 
and detection branch time, min 

Junction 1: 

13 5,14,19,15,11,12,13... 118.65 

22 5,14.19,20,21,22 94.17 

14 5, 14 4.95 

Junction 2: 

13 6, 11, 12, 13 79.27 

22 6,11,16,21,22 67.99 

14 1,5, 14 50.81 

Junction 3: 

13 7, 12, 13 37.50 

22 7,16,21,22 26.21 

14 2, 1,5, 14 70.04 

Junction 4: 

13 8, 13 12.41 

22 8, 17, 22 13.52 

14 3,2,1,5,14 77.88 

Junction 5: 

13 4, 8, 13 18.62 

22 4, 8, 17, 22 19.73 

14 4, 3, 2, 1, 5, 14 84.08 

Junction 6: 

13 14,19,15,11,12,13 115.59 

22 14,19,20,21,22 91,11 

14 14 1.89 

Junction 7: 

13 11, 12, 13 77.06 

22 11,16,21,22 65.78 

14 10, 14 76.06 

Junction 8: 

13 12, 13 36.61 

22 16,21,22 25.33 

14 12,13,9,4,3,2,1,5,14.. 120.87 

Junction 9: 

13 13 12.17 

22 17, 22 13.28 

14 13,9,4,3,2,1,5.14 96.42 

Junction 10: 

13 9, 4, 8, 13 18.79 

22 9, 4, 8, 17. 22 19.89 

14 9, 4, 3, 2, 1, 5, 14 84.25 

Junction 11: 

13 19,20,21,22,18,9,4,8.. 108.35 

22 19.20,21,22 89.22 

14 19,15,10,14 112.70 

Junction 12: 

13 20,21,22,18,9.4,8,13.. 80.02 

22 20,21,22 60.89 

14 15, 10, 14 84.37 

Junction 13: 

13 21,22,18,9,4.8,13 43.33 

22 21. 22 24.21 

14 (1) (1) 

Junction 14: 

13 22.18,9,4,8.13 31.80 

22 22 12.67 

14 22.18.9,4,3,2.1,5,14.. 97.26 

Junction 15: 

13 18, 9. 4. 8. 13 19.12 

22 18, 9, 4. 8, 17, 22 20.23 

14 18,9.4.3.2,1,5,14 84.59 

^Excessive ainways (greater than 9) in path. 

that the mesh under consideration should be composed of In order to increase the range of applicability of the 
no more airways them twice the nimiber of allowed airways computer program, several options are aveulable. The 
that can define a path. This hypothesis reqtiires additional most direct route is an increase in computer memory and 

testing. speed. An alternative is to develop a method that can be 



used to subdivide a mine network into smaller networks; 
apply the program to individual smaller networks; and 
properly synthesize the information developed from the 
smaller networks in order to develop minimum travel time 
paths for smoke in the mine. This is a subject of future 
research. 

The minimum travel time data in table 3 can be used to 
estimate the difference in smoke arrival time at the end 
of designated airways from each junction considered to be 
the location of the source fire. Figure 4 shows the relative 
differences in the smoke minimum arrival time at the end 
of airways 13, 14, and 22 for each hypothetical source 
junction. The negative sign indicates a reversal in the 
order of arrivid of smoke at the end of each of the desig- 
nated airways. 

As an example, consider a fire located at junction 11. 
According to table 3, the minimum travel time from 



junction 11 to airway 13 is 108.35 min. The m inim um 
travel time from jimction 11 to airway 22 is 89.22 min. 
The time lag between the time of first arrival of the smoke 
at the end of airways 13 and 22 is 19.13 min, and is so 
indicated in figure 4. 

It is apparent from the application presented in figure 
4 that a single pair of detectors does not uniquely deter- 
mine the fire source. A consideration of detectors only in 
airways 13 and 22 leads to a partition of the mesh into 
four zones. Each zone is defined by those airways that, if 
they contained the source fire, would produce the desig- 
nated arrival time difference at the detectors in airways 13 
and 22. The airways are determined by inspection of 
figure 4. The junctions identified with a fixed time differ- 
ence and the airflow direction in the airways associated 
with each of the junctions determines the airways that 
form a particular zone. Zone 1 contains jimctions 1 and 




NA 



Junction 
Airway 



KEY 



Time lag, min, for airways 

Airflow direction 
Not available 



'13-22 
! 13-14 
.22-14 



(19) 



19.13 

-4.35 

•23.48 



19.13 

-4.35 

■23.48 



-©r 



(14) 



24.48 

I 13.70 

89.22 



(t> 



(10) 



(15) 



I 1.28 

1.00 

- 10.28 



^ 



(5) 



24.48 

I I 3.70 

89.22 



(I) 



(6) 



<h 



11.28 
28.46 
17.18 



(20) 



-^3 



(21) 



9.12 
NA 
NA 



(II) 



<g> 



(22) 



19.13 
•65.46 
■84.59 



(16) 



11.28 
-84.26 
-95.54 



■® 



(12) 



® 



-I.I I 

-65.47 
-64,36 



(17) 



(2) 



-I.I I 
-84.25 
-83.14 



®r 



(7) 



<D 



(3) 



(8) 



^ 



11.29 
-32.54 
-43.83 



-I. II 
-65.47 
-64.36 



(13) 



(18) 



-1. 10 
-65.46 
-64.36 



® 



(4) 



(9) 



<D 



-I.II 

-65.46 
-64.35 



Figure 4.-Time lag for smoke detectors. 



6; zone 2 contains junctions 2, 3, 7, and 8; zone 3 contains 
junctions 4, 5, 9, 10, and 15; and zone 4 contains junctions 
11, 12, 13, and 14, If the corrected travel times discussed 
above were used for junctions 1 and 6, then zones 1 and 4 
would be merged into a single zone. This will not be done 
in order to examine the capability of the program with the 
retention of smjdl errors in predicted minimum travel time 
for the smoke. Figure 5 shows the partition of the mesh 
into the foiu- zones. 

The previous discussion has shown that zone 1 is in 
actuality contiguous with zone 4. The difficulty for the 
user is that a time difference in signal arrival time for 
zone 1 would lead to the user to search zone 4 for a fire. 
However, since the calculated time differences associated 
with zone 4 is closest to that for zone 1, it is reasonable to 
search for a fire source in zone 4 after completion of the 
search in zone 1. 



A similar analysis could be appUed to the pair of detec- 
tors in airways 13 zmd 14, as well as those in airways 14 
and 22. As is evident from figure 4, the network can be 
divided into approximately eight zones in each of these 
cases. However, there is uncertainty about junction 13. 
As explained earlier, airway 14 could not be reached by a 
path containing nine or less airways. For a given pair of 
detectors, the more zones the network can be divided into, 
the more accurate will be the determination of the fire 
location. 

This analysis, although subject to small error, does 
provide a method for partitioning a mesh section of a mine 
network into zones, each of which would be associated 
with a time lag between signal (smoke) arrival times at two 
detectors. 



KEY 

I; ••.•••J Zone I, 24.5 min Y / A Zone 3, -|.l min 
ESMI Zone 2, I 1.3 nnin ^3 Zone 4, 19.1 min 




Figure 5.-Partition of network into zones by lag time. 



CONCLUSIONS 



The model developed to search out all possible paths 
from a hypothetical fire source to smoke detectors in 
distinct airways and to determine the minimum smoke 
travel time to the detectors has been demonstrated to 
provide, through a compeu-ison of differences in smoke 
travel time to a pair of detectors, a rough assessment of 
the most hkely region that contJiins the fire source. A 
preliminary guideline shows its apphcability to a section of 



a mine consisting of approximately not more than 22 
airways. Additional computer memory would permit a 
direct expansion of the FORTRAN computer program in 
order to locate a fire in a larger section of a mine. An 
alternative is to develop a method that applies the program 
to individual sections of a mine and synthesizes the 
information into the construction of minrmimi travel time 
paths for the entire mine. 



10 

APPENDIX.-FORTRAN COMPUTER PROGRAM 

DISCLAIMER OF LIABILITY CLAUSE consideration by the U. S. Bureau of Mines, the user 

hereof expressly waives any and all claims for damage 

The U.S. Bureau of Mines expressly declares that there and/or suits for or by reason of personal injury, or 

are no warranties express or impUed which apply to the property damage, including special, consequential or other 

software contained herein. By acceptance £md use of similar damages arising out of or in any way connected 

said software, which is conveyed to the user without with the use of the software contained herein. 



INCLUDE 'WAY2.COM' 
TYM=SEC^fDS (0.0) 
LP=6 

CALLINPT 
DO 10 1 = 1, MSP 
IMP = ISP (I) 
DO20J=l, MST 
IBT=IST (J) 

WRITE (LP,30) IMP,IBT 
30 FORMAT (/4X,'* ********************** *y4x, 'IMP = ', 2X,I5,3X,'IBT = ',2X,I5/) 
CALL PATH (IMP) 
CALL OUTPT 
20 CONTINUE 
10 CONTINUE 

DELTA = SECNDS (TYM) 
WRITE (LP,100) DELTA 
100 FORMAT (/5X,'ELAPSED TIME = ',1X,E12.5, 2X,'SEC'/) 
STOP 
END 

SUBROUTINE MOVE (ILP) 
INCLUDE 'WAY2.COM' 
JX(1) = 1 
JX(2) = N 
JX(3) = -1 
JX(4) = -N 
IF(ILP.EQ.l) THEN 

JX(3)=0 

JX(4)=0 
ENDIF 
IF(ILP.EQ.1+(M-1)*N) THEN 

JX(2)=0 

JX(3)=0 
ENDIF 
IF(ILP.EQ.M*N) THEN 

JX(1)=0 

JX(2)=0 
ENDIF 
IF(ILP.EQ.N) THEN 

JX(1)=0 

JX(4)=0 
ENDIF 

IF(ILP.GE.2AND.ILP.LE.N-1) JX(4)=0 
IF(ILP.GE.2+(M-1)*NAND.ILP.LE.M*N-1) JX(2) = 0. 
IF(MOD(ILP,N).EQ.lAND.ILP.NE.lAND.ILP.NE.l + (M-l)*N) JX(3)=0 
IF(MOD(ILP,N).EQ.0AND.ILP.NE.NAND.ILP.NE.M*N) JX(1) =0 
RETURN 



11 



ENfD 

SUBROUTINE INPT 
INCLUDE 'WAY2.COM' 

10 = l 

OPEN(UNIT = IO,FILE = 'BRANCH.DAT'.TYPE - 'OLD') 
C *** ISP = SOURCE JUNCTION 
C **♦ 1ST = DETECTION AIRWAY 
C ♦*♦ KB = AIRWAY NO 
C *** TM = TIME IN AIRWAY 
C *** KS = FLOW DIRECTION OF AIRWAY 
C ♦** NJ = NO OF JUNCTIONS 
C *** NBT = NO OF AIRWAYS 
C **♦ DS = AIRWAY LENGTH 

C *♦* AR = CROSS SECTIONAL AREA OF AIRWAY 
C *♦* V= LINEAR FLOW VELOCITY IN AIRWAY 

READ(IO,50) MSP,MST 

READ(IO,50) (IST(I),I = 1,MSP) 

READ(IO,50) (IST(I),I = 1,MST) 
50 FORMAT (8(5X,I5)) 

WRITE (LP,50) MSP,MST 

WRITE(LP,50) (ISP(I),I = 1,MSP) 

WRITE(LP,55) 
55 FORMAT(/) 

WRITE(LP,50) (IST(I),I=1,MST) 

READ(IO,100) NJ,NBT,N,M 
100 FORMAT(5X,I5,5X,I5,5X,I5,5X,I5) 

WRITE(LP,120) NJ,NBT,N,M 
120 FORMAT(5X,'NJ = ',1X,I4,2X,'NBT = ',1X,I4,2X,'N = ',IX,I4,2X,'M = ',1X,I4/) 

DO200 J = 1,NBT 

READ(IO,300)NC(J),NA(J),NB(J),Q(J),DS(J)AR(J) 

WRITE(LP,350) J,NC(J),NA(J),NB(J),0(J),DS(J)AR(J) 
350 FORMAT(4X,'J,NC,NA,NB,O,DSAR:',4(2X,I4),3(2X,F7.0)) 

11 = NA(J) 
I2=NB(J) 
KS(I1,I2) = 1 
KS(I2,I1) = -1 
V(J) = Q(J)/AR(J) 
TM(J) = DS(J)/V(J) 
KB(I1,I2) = NC(J) 
KB(I2,I1) = KB(I1,I2) 

200 CONTINUE 

300 FORMAT(3(5X,I5),2(2X,F10.5),2X,F5.1) 

DO500J=l,NBT 

WRITE(LP,600) J,V(J),TM(J) 
500 CONTINUE 
600 FORMAT(/4X,'J,V(J),TM(J):'2X,I5,2(3X,E12.5)) 

CLOSE(UNIT=I0) 

RETURN 

END 

SUBROUTINE PATH(IPS) 

INCLUDE 'WAY2.COM' 
C *♦* PATH GENERATION 
C *** MATRIX KA(LEVEL/ELEMENT IN LEVEL) 

DO 101 = 1,4 

CALL MOVE(IMP) 

L(1,I) = IMP + JX(I) 

LO(I) = L(l,I) 



12 



M1 = (M)*(4**8) + 1 

M2=I*(4**8) 

D0 8MQ = M1,M2 

KP(MQ,1) = KS(IMP,L(1,I))*KB(L(1,I),IMP) 
8 CONTINUE 
10 CONTINUE 

DO 5 KI=2,9 

IPW=4**KI 
C *** IPW PATHS IN LEVEL KI 
C *** MOVE FROM JUNCTION ON LEVEL KI-1 TO 4 JUNCTIONS ON LEVEL KI THROUGH 4 

DIRECTIONAL MOVES 

DO 15I = 1,IPW 

J = (I-l)/4 + l 
C *** INDEX K GROUPS IPW ELEMENTS INTO GROUPS OF 4 

K=MOD(I,4) 

IF(K.EQ.O) K=4 
C *** JUNCTION LO(J) ON LEVEL KI-1 WHERE J = 1,2, ,(IPW-l)/4+ 1 

ILK=LO(J) 
C *** MOVE FROM ILK IN 4 DIRECTIONS DEHNED BY JX 

CALL MOVE (ILK) 
C *** poR EACH VALUE OF J THERE ARE 4 VALUES OF I 
C *** JUNCTION LN(I) ON LEVEL KI 

LN(I) = LO(J) + JX(K) 
C *** PATH KP FROM 'IMF FIAS AT MOST 9 ELEMENTS 

M1 = (I-1)*(4**(9-KI)) + 1 

M2=r(4**(9-KI)) 

DO20MQ = Ml,M2 

KP(MO,KI) = KS(LO(J), LN(I))*KB(LN(I),LO(J)) 
20 CONTINUE 
15 CONTINUE 

DO 12IM = 1,IPW 

LO(IM) = LN(IM) 
12 CONTINUE 
5 CONTINUE 

DO 70 1 = 1,262144 
C *** CHECK FOR PATHS IN AIRFLOW DIRECTION AND LABEL KSP= 1 

KSP(I) = 1 

D0 75JL=1,9 

IF(KP(I,JL).LT.O) KSP(I) = -1 
75 CONTINUE 
70 CONTINUE 

NSUM = 

RETURN 
C *** NSUM = # OF PATHS WITHOUT BACK TRACKING 
C *** IDENTIFY PATHS WITH AIRWAYS THAT DO NOT REPEAT 

DO 80 1 = 1,262144 

NN(I) = 1 

DO 100J1 = 1,8 

J1U=J1 + 1 

DO 200 J2=J1U,9 

IF(J1.NE J2ANDABS(KP(I,J1)).EQ ABS(KP(I,J2))) NN(I) =0 
200 CONTINUE 
100 CONTINUE 

IF(NN(I).E0.1) NSUM = NSUM + 1 
80 CONTINUE 

RETURN 

END 



13 



SUBROUTINE OUTPT 
INCLUDE 'WAY2.COM' 
WRITE(LP,5) IMP,IBT 
5 FORMAT(/4X,'IMP = ',2X,I5,3X,'IBT = ',2X,I5/) 

WRITE(LP,7) NSUM 
7 FORMAT(/4X,'NSUM = ',2X,I4/) 
C *** WRITE PATH 
C DO 10 1 = 1,16384 

C IF(NN(I).EQ.l) THEN 

C WRITE(LP,100) I,(KP(I,J),J = 1,7) 

C ENDIF 

C 10 CONTINUE 
100 FORMAT(/2X,'I = ',lX,I5,3X,'KP(y ) = ',8(2X,I5)) 
DO 20 1=1,262144 
MM(I)=0 
C *** IDENTIFY PATHS THAT CONTAIN IBT AS A AIRWAY 

DO 30 J = 1,9 
C IF(KP(I,J).EO.IBTAND.NN(I).EQ.l) THEN 

IF(KP(y).EQ.IBT) THEN 
C WRITE(LP,100) I,(KP(I,JJ),JJ = 1,9) 

MM(I) = 1 
ENDIF 
30 CONTINUE 
20 CONTINUE 
TST= 99999. 
IY=-1 
JPPY=-1 
JY=-1 

DO 200 1 = 1,262144 

IF(MM(I).EQ.1AND.KSP(I).GT.0) THEN 
TS(I) = 0. 
DO300JP=l,9 
JPP=JP 
JPX=KP(IJP) 
TS(I) = TS(I) + TM(JPX) 
IF(KP(yP).EQ.IBT) GO TO 400 
300 CONTINUE 
400 CONTINUE 
C IF(MM(I).EQ.l) WRITE(LP,900) I,MM(I)JPP,(KP(yj), 

C UJ = UPP) 

C 900 FORMAT(2X,'I,MM(I),JPP,KP(UJ):',3(2X,I6)/ 
C 18(2X,I5)) 

C WRITE(LP,500) I,TS(I),(KP(y ) J = 1 JPP) 

IF(MM(I).EQ.1AND.TS(I).LT.TST) THEN 
TST=TS(I) 
IY=I 
JY=JP 
JPPY=JPP 
ENDIF 
ENDIF 
500 FORMAT(/4X,'I = ',2X,I7,3X,'TS(I) = ',2X,E12.5/4X,'KP(I,J = 1 TO JPX):',8(2X,I7)) 
200 CONTINUE 

WRITE(LP,600) lY JY JPPY,TST,(KP(IY JJ),JJ = 1,JPPY) 
600 FORMAT(/4X,'I Y = ',1X,I7,3X,'J Y = ',1X,I7,3X,'JPPY = ',2X,I7,3X,'TST = ',2X,E12.5/4X,'KP(I Y JJ = 1 TO 
1 JPPY):',8(2X,I7)) 
RETURN 
END 



14 



IMPLICIT DOUBLE PRECISION (A-H,0-Z) 

COMMON/BLKl/JX(25),NA(25),NB(25),NC(25),MM(262144), 

1 NN(262144),KB(20,20),L(1,4), 

2 KP(262144,9) 

3 ,LO(262144),LN(262144) 

4 ,V(25)AR(25),DS(25),Q(25),TM(25), 

5 TS(262144),KS(25,25),KSP(262144) 

6 ,ISP(15),IST(15) 
COMMON/BLK2/N,M,NJ,NfBT,IMP,IBT,NSUM,MSP,MST,LP 

1 ,TYM,DELTA 



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